TORSION 121 



approximately. 



The resilience W of the spring is equal to one half the product of 

 the force P multiplied by the axial extension or compression of the 

 spring. Hence ., 



w -"- 



If the obliquity of the helix is so large that it cannot be neglected 

 in analyzing the stress, the external moment M acting at any point 

 of the helix must be resolved into two components, a torsional 

 moment lying in a plane perpendicular to the axis of the helix, 

 and a bending moment lying in a plane through the axis of the 

 helix.. Under the action of these two moments it can be shown that 

 there will be a horizontal as well as a vertical angular displace- 

 ment ; that is, if the spring is pulled, it will not only undergo axial 

 extension but will also coil up or uncoil. The result is not of suffi- 

 cient practical importance to warrant a demonstration of it being 

 given here. It may be mentioned, however, that if the wire is of 

 circular cross section, a pull will make the helix coil more closely, 

 whereas if a section of the wire is a deep and narrow rectangle, a pull 

 will make the helix uncoil. 



Problem 126. A helical spring is composed of 20 turns of steel wire .258 in. in 

 <li:um-tcr. the diameter of the coil being 3 in. If the spring is compressed by a 

 force of 60 lb., what is the maximum stress in the spring, its axial compression, and 

 silience? 



